The formation and dynamics of a laser-produced aluminum plasma have been experimentally and theoretically investigated. The visible-emitting regions of the plasma form two structures with different lifetimes and expansion velocities. The first part of the transient ionic signal simultaneously recorded by a Langmuir probe presents an oscillatory structure. A hydrodynamic model in a nondifferentiable space-time has been established. The numerical simulation of the plasma expansion showed the plasma plume separation into two patterns. Moreover, the self-structuring of the interface appears through a negative differential conductance and the current oscillations are explained as being induced by thermal fluctuations that appear in the plasma cooling processes.